Soft Inference and Posterior Marginals. September 19, 2013
|
|
- Ella Montgomery
- 6 years ago
- Views:
Transcription
1 Soft Inference and Posterior Marginals September 19, 2013
2 Soft vs. Hard Inference Hard inference Give me a single solution Viterbi algorithm Maximum spanning tree (Chu-Liu-Edmonds alg.) Soft inference Task 1: Compute a distribution over outputs Task 2: Compute functions on distribution marginal probabilities, expected values, entropies, divergences
3 Why Soft Inference? Useful applications of posterior distributions Entropy: how confused is the model? Entropy: how confused is the model of its prediction at time i? Expectations What is the expected number of words in a translation of this sentence? What is the expected number of times a word ending in ed was tagged as something other than a verb? Posterior marginals: given some input, how likely is it that some (latent) event of interest happened?
4 String Marginals Inference question for HMMs What is the probability of a string w? Answer: generate all possible tag sequences and explicitly marginalize time
5 Initial Probabilities: DET ADJ NN V Transition Probabilities: ADJ DET ADJ NN V DET NN DET ADJ NN V V Emission Probabilities: DET ADJ NN V the 0.7 green 0.1 book 0.3 might 0.2 a 0.3 big 0.4 plants 0.2 watch 0.3 old 0.4 people 0.2 watches 0.2 might 0.1 person 0.1 loves 0.1 John 0.1 reads 0.19 Examples: watch 0.1 books 0.01 John might watch NN V V the old person loves big books DET ADJ NN V ADJ NN
6 John migh watc DET tdet hdet 0.0 DET DET ADJ 0.0 DET DET NN 0.0 DET DET V 0.0 DET ADJ DET 0.0 DET ADJ ADJ 0.0 DET ADJ NN 0.0 DET ADJ V 0.0 DET NN DET 0.0 DET NN ADJ 0.0 DET NN NN 0.0 DET NN V 0.0 DET V DET 0.0 DET V ADJ 0.0 DET V NN 0.0 DET V V 0.0 John migh watc ADJ tdet hdet 0.0 ADJ DET ADJ 0.0 ADJ DET NN 0.0 ADJ DET V 0.0 ADJ ADJ DET 0.0 ADJ ADJ ADJ 0.0 ADJ ADJ NN 0.0 ADJ ADJ V 0.0 ADJ NN DET 0.0 ADJ NN ADJ 0.0 ADJ NN NN 0.0 ADJ NN V 0.0 ADJ V DET 0.0 ADJ V ADJ 0.0 ADJ V NN 0.0 ADJ V V 0.0 John migh watc NN tdet hdet 0.0 NN DET ADJ 0.0 NN DET NN 0.0 NN DET V 0.0 NN ADJ DET 0.0 NN ADJ ADJ 0.0 NN ADJ NN NN ADJ V NN NN DET 0.0 NN NN ADJ 0.0 NN NN NN 0.0 NN NN V 0.0 NN V DET 0.0 NN V ADJ 0.0 NN V NN NN V V John migh watc V tdet hdet 0.0 V DET ADJ 0.0 V DET NN 0.0 V DET V 0.0 V ADJ DET 0.0 V ADJ ADJ 0.0 V ADJ NN 0.0 V ADJ V 0.0 V NN DET 0.0 V NN ADJ 0.0 V NN NN 0.0 V NN V 0.0 V V DET 0.0 V V ADJ 0.0 V V NN 0.0 V V V 0.0
7 John migh watc DET tdet hdet 0.0 DET DET ADJ 0.0 DET DET NN 0.0 DET DET V 0.0 DET ADJ DET 0.0 DET ADJ ADJ 0.0 DET ADJ NN 0.0 DET ADJ V 0.0 DET NN DET 0.0 DET NN ADJ 0.0 DET NN NN 0.0 DET NN V 0.0 DET V DET 0.0 DET V ADJ 0.0 DET V NN 0.0 DET V V 0.0 John migh watc ADJ tdet hdet 0.0 ADJ DET ADJ 0.0 ADJ DET NN 0.0 ADJ DET V 0.0 ADJ ADJ DET 0.0 ADJ ADJ ADJ 0.0 ADJ ADJ NN 0.0 ADJ ADJ V 0.0 ADJ NN DET 0.0 ADJ NN ADJ 0.0 ADJ NN NN 0.0 ADJ NN V 0.0 ADJ V DET 0.0 ADJ V ADJ 0.0 ADJ V NN 0.0 ADJ V V 0.0 John migh watc NN tdet hdet 0.0 NN DET ADJ 0.0 NN DET NN 0.0 NN DET V 0.0 NN ADJ DET 0.0 NN ADJ ADJ 0.0 NN ADJ NN NN ADJ V NN NN DET 0.0 NN NN ADJ 0.0 NN NN NN 0.0 NN NN V 0.0 NN V DET 0.0 NN V ADJ 0.0 NN V NN NN V V John migh watc V tdet hdet 0.0 V DET ADJ 0.0 V DET NN 0.0 V DET V 0.0 V ADJ DET 0.0 V ADJ ADJ 0.0 V ADJ NN 0.0 V ADJ V 0.0 V NN DET 0.0 V NN ADJ 0.0 V NN NN 0.0 V NN V 0.0 V V DET 0.0 V V ADJ 0.0 V V NN 0.0 V V V 0.0
8 Weighted Logic Programming Slightly different notation than the textbook, but you will see it in the literature WLP is useful here because it lets us build hypergraphs
9 Weighted Logic Programming Slightly different notation than the textbook, but you will see it in the literature WLP is useful here because it lets us build hypergraphs
10 Hypergraphs
11 Hypergraphs
12 Hypergraphs
13 Item form Viterbi Algorithm
14 Viterbi Algorithm Item form Axioms
15 Viterbi Algorithm Item form Axioms Goals
16 Viterbi Algorithm Item form Axioms Goals Inference rules
17 Viterbi Algorithm Item form Axioms Goals Inference rules
18 Viterbi Algorithm w=(john, might, watch) Goal:
19 String Marginals Inference question for HMMs What is the probability of a string w? Answer: generate all possible tag sequences and explicitly marginalize time Answer: use the forward algorithm space time
20 Forward Algorithm Instead of computing a max of inputs at each node, use addition Same run-time, same space requirements Viterbi cell interpretation What is the score of the best path through the lattice ending in state q at time i? What does a forward node weight correspond to?
21 Forward Algorithm Recurrence
22 Forward Chart a i=1
23 Forward Chart a i=1
24 Forward Chart a i=1
25 Forward Chart a b i=1 i=2
26 John might watch DET ADJ NN V
27 Posterior Marginals Marginal inference question for HMMs Given x, what is the probability of being in a state q at time i? Given x, what is the probability of transitioning from state q to r at time i?
28 Posterior Marginals Marginal inference question for HMMs Given x, what is the probability of being in a state q at time i? Given x, what is the probability of transitioning from state q to r at time i?
29 Posterior Marginals Marginal inference question for HMMs Given x, what is the probability of being in a state q at time i? Given x, what is the probability of transitioning from state q to r at time i?
30 Backward Algorithm Start at the goal node(s) and work backwards through the hypergraph What is the probability in the goal node cell? What if there is more than one cell? What is the value of the axiom cell?
31 Backward Recurrence
32 Backward Chart
33 Backward Chart i=5
34 Backward Chart i=5
35 Backward Chart i=5
36 Backward Chart b i=5
37 Backward Chart b i=5
38 Backward Chart c b i=3 i=4 i=5
39 Forward-Backward Compute forward chart Compute backward chart What is?
40 Forward-Backward Compute forward chart Compute backward chart What is?
41 Edge Marginals What is the probability that x was generated and q -> r happened at time t?
42 Edge Marginals What is the probability that x was generated and q -> r happened at time t?
43 Forward-Backward a b b c b i=1 i=2 i=3 i=4 i=5
44 Generic Inference Semirings are useful structures in abstract algebra Set of values Addition, with additive identity 0: (a + 0 = a) Multiplication, with mult identity 1: (a * 1 = a) Also: a * 0 = 0 Distributivity: a * (b + c) = a * b + a * c Not required: commutativity, inverses
45 So What? You can unify Forward and Viterbi by changing the semiring
46 Semiring Inside Probability semiring marginal probability of output Counting semiring number of paths ( taggings ) Viterbi semiring best scoring derivation Log semiring w[e] = w T f(e) log(z) = log partition function
47 Semiring Edge-Marginals Probability semiring posterior marginal probability of each edge Counting semiring number of paths going through each edge Viterbi semiring score of best path going through each edge Log semiring log (sum of all exp path weights of all paths with e) = log(posterior marginal probability) + log(z)
48 Max-Marginal Pruning
49 Weighted Logic Programming Slightly different notation than the textbook, but you will see it in the literature WLP is useful here because it lets us build hypergraphs
50 Hypergraphs
51 Hypergraphs
52 Hypergraphs
53 Generalizing Forward-Backward Forward/Backward algorithms are a special case of Inside/Outside algorithms It s helpful to think of I/O as algorithms on PCFG parse forests, but it s more general Recall the 5 views of decoding: decoding is parsing More specifically, decoding is a weighted proof forest
54 Item form CKY Algorithm
55 CKY Algorithm Item form Goals
56 CKY Algorithm Item form Goals Axioms
57 CKY Algorithm Item form Goals Axioms Inference rules
58 Posterior Marginals Marginal inference question for PCFGs Given w, what is the probability of having a constituent of type Z from i to j? Given w, what is the probability of having a constituent of any type from i to j? Given w, what is the probability of using rule Z -> XY to derive the span from i to j?
59 Inside Algorithm
60 Inside Algorithm
61 Inside Algorithm
62 CKY Inside Algorithm Base case(s) Recurrence
63 Generic Inside
64 Questions for Generic Inside Probability semiring Marginal probability of input Counting semiring Number of paths (parses, labels, etc) Viterbi semiring Viterbi probability (max joint probability) Log semiring log Z(input)
65 Outside probabilities: decomposing the problem The shaded area represents the outside probability α j ( p, q) which we need to calculate. How can this be decomposed? f N pe j N pq g N ( q +1) e w 1... w p-1 w p... w q w q+1... w e w e+1... w m
66 Outside probabilities: decomposing the problem f j Step 1: We assume that N pe is the parent of N pq. Its outside probability, α f ( p, e), (represented by the yellow shading) is available recursively. How do we calculate the cross-hatched probability? f N pe j N pq g N ( q +1) e w 1... w p-1 w p... w q w q+1... w e w e+1... w m
67 Outside probabilities: decomposing the problem Step 2: The red shaded area is the inside probability g of, which is available as β g ( q + 1, e. N ( q + 1) e ) f N pe j N pq g N ( q +1) e w 1... w p-1 w p... w q w q+1... w e w e+1... w m
68 Outside probabilities: decomposing the problem Step 3: The blue shaded part corresponds to the production N f N j N g, which because of the contextfreeness of the grammar, is not dependent on the positions of the words. It s probability is simply P(N f N j N g N f, G) and is available from the PCFG without calculation. f N pe j N pq g N ( q +1) e w 1... w p-1 w p... w q w q+1... w e w e+1... w m
69 Generic Outside
70 Generic Inside-Outside
71 Inside-Outside Inside probabilities are required to compute Outside probabilities Inside-Outside works where Forward- Backward does, but not vice-versa Implementation considerations Building a hypergraph explicitly simplifies code, but it can be expensive in terms of memory
So# Inference and Posterior Marginals. September 19, 2013
So# Inference and Posterior Marginals September 19, 2013 So# vs. Hard Inference Hard inference Give me a single solucon Viterbi algorithm Maximum spanning tree (Chu- Liu- Edmonds alg.) So# inference Task
More informationNatural Language Processing CS Lecture 06. Razvan C. Bunescu School of Electrical Engineering and Computer Science
Natural Language Processing CS 6840 Lecture 06 Razvan C. Bunescu School of Electrical Engineering and Computer Science bunescu@ohio.edu Statistical Parsing Define a probabilistic model of syntax P(T S):
More informationAdvanced Natural Language Processing Syntactic Parsing
Advanced Natural Language Processing Syntactic Parsing Alicia Ageno ageno@cs.upc.edu Universitat Politècnica de Catalunya NLP statistical parsing 1 Parsing Review Statistical Parsing SCFG Inside Algorithm
More informationDecoding and Inference with Syntactic Translation Models
Decoding and Inference with Syntactic Translation Models March 5, 2013 CFGs S NP VP VP NP V V NP NP CFGs S NP VP S VP NP V V NP NP CFGs S NP VP S VP NP V NP VP V NP NP CFGs S NP VP S VP NP V NP VP V NP
More informationChapter 14 (Partially) Unsupervised Parsing
Chapter 14 (Partially) Unsupervised Parsing The linguistically-motivated tree transformations we discussed previously are very effective, but when we move to a new language, we may have to come up with
More informationNatural Language Processing
Natural Language Processing Global linear models Based on slides from Michael Collins Globally-normalized models Why do we decompose to a sequence of decisions? Can we directly estimate the probability
More informationLab 12: Structured Prediction
December 4, 2014 Lecture plan structured perceptron application: confused messages application: dependency parsing structured SVM Class review: from modelization to classification What does learning mean?
More informationSequence labeling. Taking collective a set of interrelated instances x 1,, x T and jointly labeling them
HMM, MEMM and CRF 40-957 Special opics in Artificial Intelligence: Probabilistic Graphical Models Sharif University of echnology Soleymani Spring 2014 Sequence labeling aking collective a set of interrelated
More informationProbabilistic Context-free Grammars
Probabilistic Context-free Grammars Computational Linguistics Alexander Koller 24 November 2017 The CKY Recognizer S NP VP NP Det N VP V NP V ate NP John Det a N sandwich i = 1 2 3 4 k = 2 3 4 5 S NP John
More informationLECTURER: BURCU CAN Spring
LECTURER: BURCU CAN 2017-2018 Spring Regular Language Hidden Markov Model (HMM) Context Free Language Context Sensitive Language Probabilistic Context Free Grammar (PCFG) Unrestricted Language PCFGs can
More informationContext-Free Parsing: CKY & Earley Algorithms and Probabilistic Parsing
Context-Free Parsing: CKY & Earley Algorithms and Probabilistic Parsing Natural Language Processing CS 4120/6120 Spring 2017 Northeastern University David Smith with some slides from Jason Eisner & Andrew
More informationPart of Speech Tagging: Viterbi, Forward, Backward, Forward- Backward, Baum-Welch. COMP-599 Oct 1, 2015
Part of Speech Tagging: Viterbi, Forward, Backward, Forward- Backward, Baum-Welch COMP-599 Oct 1, 2015 Announcements Research skills workshop today 3pm-4:30pm Schulich Library room 313 Start thinking about
More informationCS : Speech, NLP and the Web/Topics in AI
CS626-449: Speech, NLP and the Web/Topics in AI Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture-17: Probabilistic parsing; insideoutside probabilities Probability of a parse tree (cont.) S 1,l NP 1,2
More informationLecture 12: Algorithms for HMMs
Lecture 12: Algorithms for HMMs Nathan Schneider (some slides from Sharon Goldwater; thanks to Jonathan May for bug fixes) ENLP 17 October 2016 updated 9 September 2017 Recap: tagging POS tagging is a
More informationLecture 13: Structured Prediction
Lecture 13: Structured Prediction Kai-Wei Chang CS @ University of Virginia kw@kwchang.net Couse webpage: http://kwchang.net/teaching/nlp16 CS6501: NLP 1 Quiz 2 v Lectures 9-13 v Lecture 12: before page
More informationLecture 12: Algorithms for HMMs
Lecture 12: Algorithms for HMMs Nathan Schneider (some slides from Sharon Goldwater; thanks to Jonathan May for bug fixes) ENLP 26 February 2018 Recap: tagging POS tagging is a sequence labelling task.
More informationA* Search. 1 Dijkstra Shortest Path
A* Search Consider the eight puzzle. There are eight tiles numbered 1 through 8 on a 3 by three grid with nine locations so that one location is left empty. We can move by sliding a tile adjacent to the
More informationTopics in Natural Language Processing
Topics in Natural Language Processing Shay Cohen Institute for Language, Cognition and Computation University of Edinburgh Lecture 5 Solving an NLP Problem When modelling a new problem in NLP, need to
More informationQuiz 1, COMS Name: Good luck! 4705 Quiz 1 page 1 of 7
Quiz 1, COMS 4705 Name: 10 30 30 20 Good luck! 4705 Quiz 1 page 1 of 7 Part #1 (10 points) Question 1 (10 points) We define a PCFG where non-terminal symbols are {S,, B}, the terminal symbols are {a, b},
More informationLecture 15. Probabilistic Models on Graph
Lecture 15. Probabilistic Models on Graph Prof. Alan Yuille Spring 2014 1 Introduction We discuss how to define probabilistic models that use richly structured probability distributions and describe how
More informationNatural Language Processing : Probabilistic Context Free Grammars. Updated 5/09
Natural Language Processing : Probabilistic Context Free Grammars Updated 5/09 Motivation N-gram models and HMM Tagging only allowed us to process sentences linearly. However, even simple sentences require
More informationCOMP90051 Statistical Machine Learning
COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Trevor Cohn 24. Hidden Markov Models & message passing Looking back Representation of joint distributions Conditional/marginal independence
More informationAspects of Tree-Based Statistical Machine Translation
Aspects of Tree-Based Statistical Machine Translation Marcello Federico Human Language Technology FBK 2014 Outline Tree-based translation models: Synchronous context free grammars Hierarchical phrase-based
More informationUnit 2: Tree Models. CS 562: Empirical Methods in Natural Language Processing. Lectures 19-23: Context-Free Grammars and Parsing
CS 562: Empirical Methods in Natural Language Processing Unit 2: Tree Models Lectures 19-23: Context-Free Grammars and Parsing Oct-Nov 2009 Liang Huang (lhuang@isi.edu) Big Picture we have already covered...
More informationEmpirical Methods in Natural Language Processing Lecture 11 Part-of-speech tagging and HMMs
Empirical Methods in Natural Language Processing Lecture 11 Part-of-speech tagging and HMMs (based on slides by Sharon Goldwater and Philipp Koehn) 21 February 2018 Nathan Schneider ENLP Lecture 11 21
More informationProbabilistic Graphical Models: MRFs and CRFs. CSE628: Natural Language Processing Guest Lecturer: Veselin Stoyanov
Probabilistic Graphical Models: MRFs and CRFs CSE628: Natural Language Processing Guest Lecturer: Veselin Stoyanov Why PGMs? PGMs can model joint probabilities of many events. many techniques commonly
More informationParsing with Context-Free Grammars
Parsing with Context-Free Grammars Berlin Chen 2005 References: 1. Natural Language Understanding, chapter 3 (3.1~3.4, 3.6) 2. Speech and Language Processing, chapters 9, 10 NLP-Berlin Chen 1 Grammars
More informationA brief introduction to Conditional Random Fields
A brief introduction to Conditional Random Fields Mark Johnson Macquarie University April, 2005, updated October 2010 1 Talk outline Graphical models Maximum likelihood and maximum conditional likelihood
More informationCS460/626 : Natural Language
CS460/626 : Natural Language Processing/Speech, NLP and the Web (Lecture 27 SMT Assignment; HMM recap; Probabilistic Parsing cntd) Pushpak Bhattacharyya CSE Dept., IIT Bombay 17 th March, 2011 CMU Pronunciation
More information10 : HMM and CRF. 1 Case Study: Supervised Part-of-Speech Tagging
10-708: Probabilistic Graphical Models 10-708, Spring 2018 10 : HMM and CRF Lecturer: Kayhan Batmanghelich Scribes: Ben Lengerich, Michael Kleyman 1 Case Study: Supervised Part-of-Speech Tagging We will
More informationContext- Free Parsing with CKY. October 16, 2014
Context- Free Parsing with CKY October 16, 2014 Lecture Plan Parsing as Logical DeducBon Defining the CFG recognibon problem BoHom up vs. top down Quick review of Chomsky normal form The CKY algorithm
More informationBayesian Machine Learning - Lecture 7
Bayesian Machine Learning - Lecture 7 Guido Sanguinetti Institute for Adaptive and Neural Computation School of Informatics University of Edinburgh gsanguin@inf.ed.ac.uk March 4, 2015 Today s lecture 1
More informationLog-Linear Models with Structured Outputs
Log-Linear Models with Structured Outputs Natural Language Processing CS 4120/6120 Spring 2016 Northeastern University David Smith (some slides from Andrew McCallum) Overview Sequence labeling task (cf.
More informationLecture 12: EM Algorithm
Lecture 12: EM Algorithm Kai-Wei hang S @ University of Virginia kw@kwchang.net ouse webpage: http://kwchang.net/teaching/nlp16 S6501 Natural Language Processing 1 Three basic problems for MMs v Likelihood
More informationSTA 414/2104: Machine Learning
STA 414/2104: Machine Learning Russ Salakhutdinov Department of Computer Science! Department of Statistics! rsalakhu@cs.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 9 Sequential Data So far
More informationConditional Random Fields
Conditional Random Fields Micha Elsner February 14, 2013 2 Sums of logs Issue: computing α forward probabilities can undeflow Normally we d fix this using logs But α requires a sum of probabilities Not
More informationConditional Random Fields and beyond DANIEL KHASHABI CS 546 UIUC, 2013
Conditional Random Fields and beyond DANIEL KHASHABI CS 546 UIUC, 2013 Outline Modeling Inference Training Applications Outline Modeling Problem definition Discriminative vs. Generative Chain CRF General
More informationCS838-1 Advanced NLP: Hidden Markov Models
CS838-1 Advanced NLP: Hidden Markov Models Xiaojin Zhu 2007 Send comments to jerryzhu@cs.wisc.edu 1 Part of Speech Tagging Tag each word in a sentence with its part-of-speech, e.g., The/AT representative/nn
More informationExpectation Maximization (EM)
Expectation Maximization (EM) The EM algorithm is used to train models involving latent variables using training data in which the latent variables are not observed (unlabeled data). This is to be contrasted
More informationMidterm sample questions
Midterm sample questions CS 585, Brendan O Connor and David Belanger October 12, 2014 1 Topics on the midterm Language concepts Translation issues: word order, multiword translations Human evaluation Parts
More informationVariational Decoding for Statistical Machine Translation
Variational Decoding for Statistical Machine Translation Zhifei Li, Jason Eisner, and Sanjeev Khudanpur Center for Language and Speech Processing Computer Science Department Johns Hopkins University 1
More informationSequence Labeling: HMMs & Structured Perceptron
Sequence Labeling: HMMs & Structured Perceptron CMSC 723 / LING 723 / INST 725 MARINE CARPUAT marine@cs.umd.edu HMM: Formal Specification Q: a finite set of N states Q = {q 0, q 1, q 2, q 3, } N N Transition
More informationProbabilistic Context Free Grammars
1 Defining PCFGs A PCFG G consists of Probabilistic Context Free Grammars 1. A set of terminals: {w k }, k = 1..., V 2. A set of non terminals: { i }, i = 1..., n 3. A designated Start symbol: 1 4. A set
More informationLanguage and Statistics II
Language and Statistics II Lecture 19: EM for Models of Structure Noah Smith Epectation-Maimization E step: i,, q i # p r $ t = p r i % ' $ t i, p r $ t i,' soft assignment or voting M step: r t +1 # argma
More informationCISC 889 Bioinformatics (Spring 2004) Hidden Markov Models (II)
CISC 889 Bioinformatics (Spring 24) Hidden Markov Models (II) a. Likelihood: forward algorithm b. Decoding: Viterbi algorithm c. Model building: Baum-Welch algorithm Viterbi training Hidden Markov models
More informationCKY & Earley Parsing. Ling 571 Deep Processing Techniques for NLP January 13, 2016
CKY & Earley Parsing Ling 571 Deep Processing Techniques for NLP January 13, 2016 No Class Monday: Martin Luther King Jr. Day CKY Parsing: Finish the parse Recognizer à Parser Roadmap Earley parsing Motivation:
More informationStatistical Methods for NLP
Statistical Methods for NLP Information Extraction, Hidden Markov Models Sameer Maskey Week 5, Oct 3, 2012 *many slides provided by Bhuvana Ramabhadran, Stanley Chen, Michael Picheny Speech Recognition
More informationStatistical Methods for NLP
Statistical Methods for NLP Sequence Models Joakim Nivre Uppsala University Department of Linguistics and Philology joakim.nivre@lingfil.uu.se Statistical Methods for NLP 1(21) Introduction Structured
More informationExpectation Maximization (EM)
Expectation Maximization (EM) The Expectation Maximization (EM) algorithm is one approach to unsupervised, semi-supervised, or lightly supervised learning. In this kind of learning either no labels are
More informationParsing with CFGs L445 / L545 / B659. Dept. of Linguistics, Indiana University Spring Parsing with CFGs. Direction of processing
L445 / L545 / B659 Dept. of Linguistics, Indiana University Spring 2016 1 / 46 : Overview Input: a string Output: a (single) parse tree A useful step in the process of obtaining meaning We can view the
More informationParsing with CFGs. Direction of processing. Top-down. Bottom-up. Left-corner parsing. Chart parsing CYK. Earley 1 / 46.
: Overview L545 Dept. of Linguistics, Indiana University Spring 2013 Input: a string Output: a (single) parse tree A useful step in the process of obtaining meaning We can view the problem as searching
More informationHidden Markov Models
CS769 Spring 2010 Advanced Natural Language Processing Hidden Markov Models Lecturer: Xiaojin Zhu jerryzhu@cs.wisc.edu 1 Part-of-Speech Tagging The goal of Part-of-Speech (POS) tagging is to label each
More informationStatistical NLP for the Web Log Linear Models, MEMM, Conditional Random Fields
Statistical NLP for the Web Log Linear Models, MEMM, Conditional Random Fields Sameer Maskey Week 13, Nov 28, 2012 1 Announcements Next lecture is the last lecture Wrap up of the semester 2 Final Project
More informationSTA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.utstat.utoronto.ca/~rsalakhu/ Sidney Smith Hall, Room 6002 Lecture 11 Project
More informationHidden Markov Models
Hidden Markov Models Slides mostly from Mitch Marcus and Eric Fosler (with lots of modifications). Have you seen HMMs? Have you seen Kalman filters? Have you seen dynamic programming? HMMs are dynamic
More informationCS460/626 : Natural Language
CS460/626 : Natural Language Processing/Speech, NLP and the Web (Lecture 23, 24 Parsing Algorithms; Parsing in case of Ambiguity; Probabilistic Parsing) Pushpak Bhattacharyya CSE Dept., IIT Bombay 8 th,
More informationDecoding Revisited: Easy-Part-First & MERT. February 26, 2015
Decoding Revisited: Easy-Part-First & MERT February 26, 2015 Translating the Easy Part First? the tourism initiative addresses this for the first time the die tm:-0.19,lm:-0.4, d:0, all:-0.65 tourism touristische
More informationMore on HMMs and other sequence models. Intro to NLP - ETHZ - 18/03/2013
More on HMMs and other sequence models Intro to NLP - ETHZ - 18/03/2013 Summary Parts of speech tagging HMMs: Unsupervised parameter estimation Forward Backward algorithm Bayesian variants Discriminative
More informationMATH 556: PROBABILITY PRIMER
MATH 6: PROBABILITY PRIMER 1 DEFINITIONS, TERMINOLOGY, NOTATION 1.1 EVENTS AND THE SAMPLE SPACE Definition 1.1 An experiment is a one-off or repeatable process or procedure for which (a there is a well-defined
More informationLog-Linear Models, MEMMs, and CRFs
Log-Linear Models, MEMMs, and CRFs Michael Collins 1 Notation Throughout this note I ll use underline to denote vectors. For example, w R d will be a vector with components w 1, w 2,... w d. We use expx
More informationStatistical Methods for NLP
Statistical Methods for NLP Stochastic Grammars Joakim Nivre Uppsala University Department of Linguistics and Philology joakim.nivre@lingfil.uu.se Statistical Methods for NLP 1(22) Structured Classification
More informationHidden Markov Models. By Parisa Abedi. Slides courtesy: Eric Xing
Hidden Markov Models By Parisa Abedi Slides courtesy: Eric Xing i.i.d to sequential data So far we assumed independent, identically distributed data Sequential (non i.i.d.) data Time-series data E.g. Speech
More informationMachine Learning & Data Mining Caltech CS/CNS/EE 155 Hidden Markov Models Last Updated: Feb 7th, 2017
1 Introduction Let x = (x 1,..., x M ) denote a sequence (e.g. a sequence of words), and let y = (y 1,..., y M ) denote a corresponding hidden sequence that we believe explains or influences x somehow
More informationDependency Parsing. Statistical NLP Fall (Non-)Projectivity. CoNLL Format. Lecture 9: Dependency Parsing
Dependency Parsing Statistical NLP Fall 2016 Lecture 9: Dependency Parsing Slav Petrov Google prep dobj ROOT nsubj pobj det PRON VERB DET NOUN ADP NOUN They solved the problem with statistics CoNLL Format
More informationProbability, Entropy, and Inference / More About Inference
Probability, Entropy, and Inference / More About Inference Mário S. Alvim (msalvim@dcc.ufmg.br) Information Theory DCC-UFMG (2018/02) Mário S. Alvim (msalvim@dcc.ufmg.br) Probability, Entropy, and Inference
More informationProcessing/Speech, NLP and the Web
CS460/626 : Natural Language Processing/Speech, NLP and the Web (Lecture 25 Probabilistic Parsing) Pushpak Bhattacharyya CSE Dept., IIT Bombay 14 th March, 2011 Bracketed Structure: Treebank Corpus [ S1[
More informationDoctoral Course in Speech Recognition. May 2007 Kjell Elenius
Doctoral Course in Speech Recognition May 2007 Kjell Elenius CHAPTER 12 BASIC SEARCH ALGORITHMS State-based search paradigm Triplet S, O, G S, set of initial states O, set of operators applied on a state
More informationBasic math for biology
Basic math for biology Lei Li Florida State University, Feb 6, 2002 The EM algorithm: setup Parametric models: {P θ }. Data: full data (Y, X); partial data Y. Missing data: X. Likelihood and maximum likelihood
More informationSpectral Learning for Non-Deterministic Dependency Parsing
Spectral Learning for Non-Deterministic Dependency Parsing Franco M. Luque 1 Ariadna Quattoni 2 Borja Balle 2 Xavier Carreras 2 1 Universidad Nacional de Córdoba 2 Universitat Politècnica de Catalunya
More informationConditional Random Field
Introduction Linear-Chain General Specific Implementations Conclusions Corso di Elaborazione del Linguaggio Naturale Pisa, May, 2011 Introduction Linear-Chain General Specific Implementations Conclusions
More information{Probabilistic Stochastic} Context-Free Grammars (PCFGs)
{Probabilistic Stochastic} Context-Free Grammars (PCFGs) 116 The velocity of the seismic waves rises to... S NP sg VP sg DT NN PP risesto... The velocity IN NP pl of the seismic waves 117 PCFGs APCFGGconsists
More information9 Forward-backward algorithm, sum-product on factor graphs
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.438 Algorithms For Inference Fall 2014 9 Forward-backward algorithm, sum-product on factor graphs The previous
More informationAN ABSTRACT OF THE DISSERTATION OF
AN ABSTRACT OF THE DISSERTATION OF Kai Zhao for the degree of Doctor of Philosophy in Computer Science presented on May 30, 2017. Title: Structured Learning with Latent Variables: Theory and Algorithms
More informationIntelligent Systems (AI-2)
Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 19 Oct, 24, 2016 Slide Sources Raymond J. Mooney University of Texas at Austin D. Koller, Stanford CS - Probabilistic Graphical Models D. Page,
More informationCRF for human beings
CRF for human beings Arne Skjærholt LNS seminar CRF for human beings LNS seminar 1 / 29 Let G = (V, E) be a graph such that Y = (Y v ) v V, so that Y is indexed by the vertices of G. Then (X, Y) is a conditional
More informationParsing. Probabilistic CFG (PCFG) Laura Kallmeyer. Winter 2017/18. Heinrich-Heine-Universität Düsseldorf 1 / 22
Parsing Probabilistic CFG (PCFG) Laura Kallmeyer Heinrich-Heine-Universität Düsseldorf Winter 2017/18 1 / 22 Table of contents 1 Introduction 2 PCFG 3 Inside and outside probability 4 Parsing Jurafsky
More informationLinear Dynamical Systems
Linear Dynamical Systems Sargur N. srihari@cedar.buffalo.edu Machine Learning Course: http://www.cedar.buffalo.edu/~srihari/cse574/index.html Two Models Described by Same Graph Latent variables Observations
More informationLecture 3: ASR: HMMs, Forward, Viterbi
Original slides by Dan Jurafsky CS 224S / LINGUIST 285 Spoken Language Processing Andrew Maas Stanford University Spring 2017 Lecture 3: ASR: HMMs, Forward, Viterbi Fun informative read on phonetics The
More informationThis kind of reordering is beyond the power of finite transducers, but a synchronous CFG can do this.
Chapter 12 Synchronous CFGs Synchronous context-free grammars are a generalization of CFGs that generate pairs of related strings instead of single strings. They are useful in many situations where one
More informationSequence Modelling with Features: Linear-Chain Conditional Random Fields. COMP-599 Oct 6, 2015
Sequence Modelling with Features: Linear-Chain Conditional Random Fields COMP-599 Oct 6, 2015 Announcement A2 is out. Due Oct 20 at 1pm. 2 Outline Hidden Markov models: shortcomings Generative vs. discriminative
More informationHidden Markov Models. Aarti Singh Slides courtesy: Eric Xing. Machine Learning / Nov 8, 2010
Hidden Markov Models Aarti Singh Slides courtesy: Eric Xing Machine Learning 10-701/15-781 Nov 8, 2010 i.i.d to sequential data So far we assumed independent, identically distributed data Sequential data
More informationQuasi-Synchronous Phrase Dependency Grammars for Machine Translation. lti
Quasi-Synchronous Phrase Dependency Grammars for Machine Translation Kevin Gimpel Noah A. Smith 1 Introduction MT using dependency grammars on phrases Phrases capture local reordering and idiomatic translations
More informationHidden Markov Models. Terminology and Basic Algorithms
Hidden Markov Models Terminology and Basic Algorithms The next two weeks Hidden Markov models (HMMs): Wed 9/11: Terminology and basic algorithms Mon 14/11: Implementing the basic algorithms Wed 16/11:
More informationlecture 6: modeling sequences (final part)
Natural Language Processing 1 lecture 6: modeling sequences (final part) Ivan Titov Institute for Logic, Language and Computation Outline After a recap: } Few more words about unsupervised estimation of
More information6.864: Lecture 5 (September 22nd, 2005) The EM Algorithm
6.864: Lecture 5 (September 22nd, 2005) The EM Algorithm Overview The EM algorithm in general form The EM algorithm for hidden markov models (brute force) The EM algorithm for hidden markov models (dynamic
More informationwith Local Dependencies
CS11-747 Neural Networks for NLP Structured Prediction with Local Dependencies Xuezhe Ma (Max) Site https://phontron.com/class/nn4nlp2017/ An Example Structured Prediction Problem: Sequence Labeling Sequence
More informationFinal Exam, Machine Learning, Spring 2009
Name: Andrew ID: Final Exam, 10701 Machine Learning, Spring 2009 - The exam is open-book, open-notes, no electronics other than calculators. - The maximum possible score on this exam is 100. You have 3
More informationCOMS 4771 Probabilistic Reasoning via Graphical Models. Nakul Verma
COMS 4771 Probabilistic Reasoning via Graphical Models Nakul Verma Last time Dimensionality Reduction Linear vs non-linear Dimensionality Reduction Principal Component Analysis (PCA) Non-linear methods
More informationIntroduction to Machine Learning CMU-10701
Introduction to Machine Learning CMU-10701 Hidden Markov Models Barnabás Póczos & Aarti Singh Slides courtesy: Eric Xing i.i.d to sequential data So far we assumed independent, identically distributed
More informationProbabilistic Graphical Models
Probabilistic Graphical Models Brown University CSCI 2950-P, Spring 2013 Prof. Erik Sudderth Lecture 12: Gaussian Belief Propagation, State Space Models and Kalman Filters Guest Kalman Filter Lecture by
More informationData-Intensive Computing with MapReduce
Data-Intensive Computing with MapReduce Session 8: Sequence Labeling Jimmy Lin University of Maryland Thursday, March 14, 2013 This work is licensed under a Creative Commons Attribution-Noncommercial-Share
More informationCMPT-825 Natural Language Processing. Why are parsing algorithms important?
CMPT-825 Natural Language Processing Anoop Sarkar http://www.cs.sfu.ca/ anoop October 26, 2010 1/34 Why are parsing algorithms important? A linguistic theory is implemented in a formal system to generate
More informationHierarchical Bayesian Nonparametrics
Hierarchical Bayesian Nonparametrics Micha Elsner April 11, 2013 2 For next time We ll tackle a paper: Green, de Marneffe, Bauer and Manning: Multiword Expression Identification with Tree Substitution
More informationMultilevel Coarse-to-Fine PCFG Parsing
Multilevel Coarse-to-Fine PCFG Parsing Eugene Charniak, Mark Johnson, Micha Elsner, Joseph Austerweil, David Ellis, Isaac Haxton, Catherine Hill, Shrivaths Iyengar, Jeremy Moore, Michael Pozar, and Theresa
More informationIntelligent Systems (AI-2)
Intelligent Systems (AI-2) Computer Science cpsc422, Lecture 19 Oct, 23, 2015 Slide Sources Raymond J. Mooney University of Texas at Austin D. Koller, Stanford CS - Probabilistic Graphical Models D. Page,
More informationStatistical Machine Translation
Statistical Machine Translation -tree-based models (cont.)- Artem Sokolov Computerlinguistik Universität Heidelberg Sommersemester 2015 material from P. Koehn, S. Riezler, D. Altshuler Bottom-Up Decoding
More informationParsing with Context-Free Grammars
Parsing with Context-Free Grammars CS 585, Fall 2017 Introduction to Natural Language Processing http://people.cs.umass.edu/~brenocon/inlp2017 Brendan O Connor College of Information and Computer Sciences
More informationMarrying Dynamic Programming with Recurrent Neural Networks
Marrying Dynamic Programming with Recurrent Neural Networks I eat sushi with tuna from Japan Liang Huang Oregon State University Structured Prediction Workshop, EMNLP 2017, Copenhagen, Denmark Marrying
More informationMachine Learning for OR & FE
Machine Learning for OR & FE Hidden Markov Models Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com Additional References: David
More informationNatural Language Processing Prof. Pawan Goyal Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Natural Language Processing Prof. Pawan Goyal Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture - 18 Maximum Entropy Models I Welcome back for the 3rd module
More information